Subgroups — C₁₃×2₋¹⁺⁴⋊C₃ #11929258

Order 1248.

92 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#41⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×SL(2,𝔽₃)	C₂	1	2	yes	maximal, complemented
3	C₁₃×2₋¹⁺⁴	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₃×D₄×C₁₃	—	4	1	no	maximal
5	C₁₃×SL(2,𝔽₃)	C₂²	1	1	yes	characteristic
6	C₁₃×#41	—	3	1	no	—
7	C₁₃×#41	—	3	2	no	—
8	C₁₃×#41	C₂×C₃	1	1	yes	characteristic, complemented
9	C₂×Q₈×C₁₃	—	3	1	no	—
10	C₂×Q₈×C₁₃	C₂×C₃	1	2	yes	complemented
11	C₂²×C₃×C₁₃	—	4	2	no	—
12	C₃×C₄×C₁₃	—	4	1	no	—
13	Q₈×C₁₃	—	3	1	no	—
14	Q₈×C₁₃	—	3	2	no	—
15	Q₈×C₁₃	C₂²×C₃	1	1	yes	characteristic
16	D₄×C₁₃	—	3	2	no	—
17	D₄×C₁₃	—	3	1	no	—
18	D₄×C₁₃	A₄	1	1	yes	characteristic
19	C₂×C₄×C₁₃	—	3	2	no	—
20	C₂×C₄×C₁₃	—	3	2	no	—
21	C₂×C₄×C₁₃	—	3	1	no	—
22	2₋¹⁺⁴⋊C₃	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
23	C₂×C₃×C₁₃	—	4	1	no	—
24	C₂×C₃×C₁₃	—	8	2	no	—
25	C₂²×C₁₃	—	3	1	no	—
26	C₂²×C₁₃	C₂×A₄	1	2	yes	—
27	C₄×C₁₃	—	3	2	no	—
28	C₄×C₁₃	—	3	1	no	—
29	C₄×C₁₃	C₂×A₄	1	1	yes	characteristic
30	#41⋊C₃	C₂×C₁₃	1	1	yes	characteristic, complemented
31	C₂×SL(2,𝔽₃)	C₂×C₁₃	1	2	yes	complemented
32	C₃×C₁₃	—	4	1	no	Hall
33	2₋¹⁺⁴	C₃×C₁₃	1	1	yes	characteristic, complemented, Sylow
34	C₂×C₁₃	—	2	2	no	—
35	C₂×C₁₃	—	6	1	no	—
36	C₂×C₁₃	C₂²×A₄	1	1	yes	characteristic
37	C₃×D₄	—	4	1	no	—
38	SL(2,𝔽₃)	C₂²×C₁₃	1	1	yes	characteristic
39	#41	—	3	1	no	—
40	#41	—	3	2	no	—
41	#41	C₂×C₃×C₁₃	1	1	yes	characteristic, complemented
42	C₂×Q₈	—	3	1	no	—
43	C₂×Q₈	C₂×C₃×C₁₃	1	2	yes	complemented
44	C₁₃	2₋¹⁺⁴⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
45	C₂²×C₃	—	4	2	no	—
46	C₃×C₄	—	4	1	no	—
47	Q₈	—	3	2	no	—
48	Q₈	—	3	1	no	—
49	Q₈	C₂²×C₃×C₁₃	1	1	yes	characteristic
50	D₄	—	3	1	no	—
51	D₄	—	3	2	no	—
52	D₄	A₄×C₁₃	1	1	yes	characteristic
53	C₂×C₄	—	3	2	no	—
54	C₂×C₄	—	3	2	no	—
55	C₂×C₄	—	3	1	no	—
56	C₂×C₃	—	4	1	no	—
57	C₂×C₃	—	8	2	no	—
58	C₂²	—	3	1	no	—
59	C₂²	C₂×A₄×C₁₃	1	2	yes	—
60	C₄	—	3	2	no	—
61	C₄	—	3	1	no	—
62	C₄	C₂×A₄×C₁₃	1	1	yes	characteristic
63	C₃	—	4	1	no	Sylow
64	C₂	—	2	2	no	—
65	C₂	—	6	1	no	—
66	C₂	C₂²×A₄×C₁₃	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₃	C₂²×A₄
commutator, cosocle, hypocenter	Q₈	C₂²×C₃×C₁₃
Frattini	C₂	C₂²×A₄×C₁₃
Fitting	C₁₃×2₋¹⁺⁴	C₃
hypercenter	D₄×C₁₃	A₄
LCS	G ▷ Q₈
UCS	C₁ ◁ C₂×C₁₃ ◁ D₄×C₁₃

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₁₃×#41⋊C₃	C₂	semidirect
2. C₂×C₁₃×SL(2,𝔽₃)	C₂	semidirect
3. C₁₃×2₋¹⁺⁴	C₃	semidirect
8. C₁₃×#41	C₂×C₃	semidirect
10. C₂×Q₈×C₁₃	C₂×C₃	semidirect
22. 2₋¹⁺⁴⋊C₃	C₁₃	direct (N × H)
30. #41⋊C₃	C₂×C₁₃	semidirect
31. C₂×SL(2,𝔽₃)	C₂×C₁₃	semidirect
33. 2₋¹⁺⁴	C₃×C₁₃	semidirect
41. #41	C₂×C₃×C₁₃	semidirect
43. C₂×Q₈	C₂×C₃×C₁₃	semidirect
44. C₁₃	2₋¹⁺⁴⋊C₃	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₁₃×#41⋊C₃	2
C₂×C₁₃×SL(2,𝔽₃)	2
C₁₃×2₋¹⁺⁴	3
C₃×D₄×C₁₃	4
2₋¹⁺⁴⋊C₃	13

Subgroups — C13×2−1+4⋊C3 #11929258

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×2₋¹⁺⁴⋊C₃ #11929258